TY - JOUR
T1 - Evaluation and prediction of polygon approximations of planar contours for shape analysis
AU - Prematilake, Chalani
AU - Ellingson, Leif
N1 - Publisher Copyright:
© 2017 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2018/5/19
Y1 - 2018/5/19
N2 - Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis. Practically speaking, each observed contour, while theoretically infinite dimensional, must be discretized for computations. As such, the coordinates for each contour as obtained at k sampling times, resulting in the contour being represented as a k-dimensional complex vector. While choosing large values of k will result in closer approximations to the original contour, this will also result in higher computational costs in the subsequent analysis. The goal of this study is to determine reasonable values for k so as to keep the computational cost low while maintaining accuracy. To do this, we consider two methods for selecting sample points and determine lower bounds for k for obtaining a desired level of approximation error using two different criteria. Because this process is computationally inefficient to perform on a large scale, we then develop models for predicting the lower bounds for k based on simple characteristics of the contours.
AB - Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis. Practically speaking, each observed contour, while theoretically infinite dimensional, must be discretized for computations. As such, the coordinates for each contour as obtained at k sampling times, resulting in the contour being represented as a k-dimensional complex vector. While choosing large values of k will result in closer approximations to the original contour, this will also result in higher computational costs in the subsequent analysis. The goal of this study is to determine reasonable values for k so as to keep the computational cost low while maintaining accuracy. To do this, we consider two methods for selecting sample points and determine lower bounds for k for obtaining a desired level of approximation error using two different criteria. Because this process is computationally inefficient to perform on a large scale, we then develop models for predicting the lower bounds for k based on simple characteristics of the contours.
KW - Shape analysis
KW - dimension reduction
KW - planar contours
KW - polygon approximations
KW - prediction of lower bounds
UR - http://www.scopus.com/inward/record.url?scp=85027509950&partnerID=8YFLogxK
U2 - 10.1080/02664763.2017.1364716
DO - 10.1080/02664763.2017.1364716
M3 - Article
AN - SCOPUS:85027509950
SN - 0266-4763
VL - 45
SP - 1227
EP - 1246
JO - Journal of Applied Statistics
JF - Journal of Applied Statistics
IS - 7
ER -